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Title: Friends Not Foes: Strong Correlation Between Inner Super-Earths and Outer Gas Giants
Authors: Marta L. Bryan and Eve J. Lee
Authors’ Institutions: University of Toronto and McGill University
Status: Published in ApJL
We have found exoplanet systems with small, close-in planets, like super-Earths, and we have also found exoplanet systems with distant gas giants like Jupiter. However, it is not clear how often these two kinds of planets form in the same planetary system. A system with a small, close-in planet and a distant giant planet would begin to resemble our own solar system, in that we have multiple rocky planets interior to multiple gas giant planets. We have found a few of these systems, and when astronomers find a few of something, they naturally want to compute an occurrence rate (see this bite).
Today’s article looks at the occurrence rates of small and large planets in the same system. Occurrence rates attempt to quantify how often a particular outcome is expected to be observed. In exoplanet science, this represents how often a particular kind of planet will be found if one randomly surveys stars to search for planets. In particular, today’s article looks to settle a debate. In the past, multiple teams have attempted to measure the occurrence rate of systems with a distant gas giant planet, given that the system has an inner small planet. We call this the conditional occurrence rate, because we want to know how often Planet Type A will be found in a chosen system if we already know (i.e., “on the condition”) that Planet Type B occurs in that chosen system.
Three past studies found a positive correlation between the conditional occurrence of these kinds of planets. In other words, if you find an inner small planet, you are more likely to find a distant giant than you would be if you randomly looked at a system with no inner small planet. However, other studies found no correlation (see this astrobite) or an anti-correlation — that is, you are less likely to find a distant gas giant in a system with an inner small planet than in a system with no inner small planet. It was recently found that accounting for the metallicity of the host stars results in a positive correlation instead of no correlation or a negative correlation. Metallicity is the measurement of how much of the star is composed of elements heavier than helium. Higher metallicity means a higher percentage of the star is made up of heavy elements, or “metals.”
Today’s article builds on the finding that host-star metallicity is an important metric for properly understanding the conditional occurrence rate of small, close-in planets and distant gas giant planets. The authors take all stars that have large publicly available radial velocity data sets and at least one confirmed small, close-in planet. They also purposefully cut out any host stars that are M dwarfs, since it has been demonstrated that M-dwarf stars have almost no distant gas giants (see this astrobite). Ultimately, they compile a sample of 184 systems.
To calculate the conditional occurrence rate, the authors have to take into account the completeness of the radial velocity data sets for finding distant giants. Completeness quantifies how sensitive the data are to finding a certain kind of planet (see this astrobite). For example, the radial velocities may have been sampled at times that are inopportune to finding a certain mass and period planet. To measure completeness for each of their 184 systems, the authors perform an injection/recovery test. They generate a planet with a given set of orbital parameters (period, eccentricity, inclination) and mass, then generate (inject) the expected radial velocity curve for that simulated planet at the same timestamps as the real observations. They then attempt to detect the simulated planet in the simulated data (recover).
They do this thousands of times for different simulated planets and repeat this for each of the 184 data sets. From this test, they can quantify how many distant giant planets these data sets might have missed and how many they almost definitely did not miss. Using these completeness maps, they generate an average completion map (see Figure 1), which they use to compute the conditional occurrence rate.
Figure 1: The color bar shows the average completeness map for this sample (bright colors are more complete, dark colors are less complete) with the detected distant gas giant planets overlaid as blue dots. [Adapted from Bryan & Lee 2024]
But this is not quite enough — we also need to compare the conditional occurrence rate to the occurrence rate of distant gas giant planets, regardless of having an inner planet or not. If the rates are different, that tells us there is a relationship between the inner and outer system planets. Indeed the authors do find different rates! For metal-rich stars, they find that regardless of the inner system, distant giant planets occur for 12–13% of stars. (The authors used two data sets for this analysis.) Distant giant planets occur for 4–6% of metal-poor stars. Therefore, because the conditional occurrence is enhanced (28% vs. 12–13%, see Figure 2), this points to a positive correlation: if you find an inner small planet, you are more likely to find a distant gas giant than if you randomly searched for only distant gas giants!
Figure 2: The probability distribution of the conditional occurrence rates for systems with inner small planets (red) versus without considering any inner planets (black and gray). The red curve peaks at a higher occurrence rate than the black and gray curves, so having an inner small planet enhances the occurrence of having a distant gas giant. [Adapted from Bryan & Lee 2024]
Original astrobite edited by Samantha Wong.
About the author, Jack Lubin:
Jack received his PhD in astrophysics from UC Irvine and is now a postdoc at UCLA. His research focuses on exoplanet detection and characterization, primarily using the radial velocity method. He enjoys communicating science and encourages everyone to be an observer of the world around them.